Particle systems with lamps as the object emitted
It is nothing about particle system actually.

As you see, there are some non-mesh type of objects cannot be rendered, such as lamps/bones/cameras/lattices/empties, etc, since they don't have any solid face to render. However, you can still see their effects around the scene as ususal.

Anyway, other options here would be: 

For BI:


Instead of lamp, use mesh object with Emit shading enabled;
Group lamp with mesh object, set mesh material type to Halo, emit the whole group as particle unit.


For Cycles:


Use mesh object as particle unit, use Emission shader for material setting. (recommended)